How to scale Faces evenly?
What you need is the "Inset" tool. This tool has an "Outset" option which works for your situation. 


First select the face 
Press I then hit Enter
Either press F6 to bring up the operator settings or go to the Tool Shelf (if it's not visible bring it up using T)
Check the Outset option.
In the operator settings, increase the Depth as desired.




Update

If you don't want the height to change, simply set the snap element to "Vertex" and move the face in the z-axis while holding the Ctrl key.